Abstract
The current work is done in the framework of the BMBF (Bundesministerium für Bildung und Forschung - the Federal Ministry of Education and Research) project AdaptHydroMod - Adaptive Hydrological Modelling with Application in Water Industry [1], which is devoted to the development of generic adaptive approach to modelling of coupled hydrological processes: surface and groundwater flows. The surface water flow is modelled by the two-dimensional shallow water equations and the surface flow - by the Richards equation. The implementation is based within DUNE - the Distributed and Unified Numerics Environment [14]. The surface flow, on which we focus in the presented paper, is numerically solved using the Runge-Kutta discontinuous Galerkin method [10] with modifications to render the scheme well-balanced and for handling correctly possible wetting and drying processes. The newly developed limiter [12] is used for the stabilization of the method. The validation of the code is done using several test problems with known exact solutions. The problem with a mass source term, which is a first step to the coupled simulation of the surface and groundwater flows, is solved numerically.
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Dedner, A., Kröner, D., Shokina, N. (2011). Adaptive Modelling of Two-Dimensional Shallow Water Flows with Wetting and Drying. In: Krause, E., Shokin, Y., Resch, M., Kröner, D., Shokina, N. (eds) Computational Science and High Performance Computing IV. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17770-5_1
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DOI: https://doi.org/10.1007/978-3-642-17770-5_1
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